1. Field of the Invention
The present invention relates to an optical sensing device, especially to a non-contact optical sensing device and method for sensing depth of an object in three-dimensional space.
2. Description of the Prior Arts
With the progress of the technology, electronic products change with each passing day. The ways to input data or command into the electronic products also advance. From the traditional physical keyboard as an input way, it develops to input with a virtual keyboard in touch panel. Recently, a non-contact way to input is also developed. The user does not need to touch the electronic device. The electronic device detects and identifies the user's gesture performing in the air through a non-contact sensor to execute a corresponding command. Especially to an apparatus that has an augmented reality (AR) function, using non-contact input is more intuitive and more convenient. Conventional non-contact sense mainly include two different ways. One way is to use proximity-sensing (PS) and another way is to use time-of-flight (TOF) sensing.
The PS procedure utilizes the optical elements to emit light on the objects to generate reflected light and utilizes the energies of the reflected light to determine the depth of the objects. However, since the objects with different colors absorb the energies of light differently, the different objects at the same depth may be determined as locating at different depths. For example, when the user has metal ornaments worn on the fingers, the depths of the fingers and the metal ornaments are determined as locating at different depths since the meal ornaments and the fingers absorb energies of light differently. Therefore, using the PS procedure easily results in the misjudgment of the depths of the objects.
The TOF sensing procedure utilizes the optical elements to emit light on the objects to generate reflected light and utilizes the time difference between the emitting time of the light and the receiving time of the reflected light to determine the depths of the objects. Since the velocity of light is not influenced by the absorbed energies of the objects, the depth determined by the TOF sensing procedure is more accurate than the depth determined by the PS procedure.
However, the reliability of the determined depth of the TOF sensing procedure has a larger tolerance scope than the reliability of the determined depth of the PS procedure according to the following formulas.
The TOF sensing procedure calculates the depth based on the data measured at different phases. The formula to calculate the tolerance scope δd of the depth d of the object is shown as following:
      d    =                  c        ⁢                                  ⁢        δ        ⁢                                  ⁢        T            =                                    c            ω                    ⁢          ϕ                =                                            c              ω                        ⁢                          tan                              -                1                                      ⁢                                          Q                0                                            Q                90                                              ≈                                    c              ω                        ⁢                                          Q                0                                            Q                90                                                                    δ      ⁢                          ⁢      d        =                  c        ω            ⁢              (                                            δ              ⁢                                                          ⁢                              Q                0                                                    Q              90                                -                                                    Q                0                            ⁢              δ              ⁢                                                          ⁢                              Q                90                                                    Q              90              2                                      )                                δ        ⁢                                  ⁢        d            d        =                                        Q            90                                Q            0                          ⁢                  (                                                    δ                ⁢                                                                  ⁢                                  Q                  0                                                            Q                90                                      -                                                            Q                  0                                ⁢                δ                ⁢                                                                  ⁢                                  Q                  90                                                            Q                90                2                                              )                    =                                    δ            ⁢                                                  ⁢                          Q              0                                            Q            0                          -                              δ            ⁢                                                  ⁢                          Q              90                                            Q            90                                          σ      ⁡              (                              δ            ⁢                                                  ⁢            d                    d                )              =                                        σ            2                    ⁡                      (                                          σ                ⁢                                                                  ⁢                                  Q                  0                                                            Q                0                                      )                          +                              σ            2                    ⁡                      (                                          σ                ⁢                                                                  ⁢                                  Q                  90                                                            Q                90                                      )                              
The Poisson distribution of the TOF sensing procedure is:
            σ      ⁡              (                  Q                      δ            ⁢                                                  ⁢            Q                          )              ->                  N            ⁢                          ⁢      where      ⁢                          ⁢      N        =      Q    q  
The unreliability of the depth is:
            σ      ⁢              (                              δ            ⁢                                                  ⁢            d                    d                )              =                                        1                          N              0                                +                      1                          N              90                                          =                        1                                    (                                                SNR                  0                                SNR                            )                        ⁢                          (                                                SNR                  90                                SNR                            )                                      ⁢                  1          SNR                                1                        (                                    SNR              0                        SNR                    )                ⁢                  (                                    SNR              90                        SNR                    )                      >    1  
The “N0” and “N99” represents the amount of the photons at the 0 degrees phase and 90 degrees phase. Therefore, the formula represents the nonlinear relationship between the unreliability of the depth and the amount of the photons.
On the other hand, the PS procedure calculates the depth of the object based on the intensity of the reflected light. The formula of the PS procedure is as following:
      Q    =          K              d        2                        δ      ⁢                          ⁢      Q        =                  K        ⁡                  (                                    -              2                        ⁢                          1                              d                3                                              )                    ⁢      δ      ⁢                          ⁢      d                                    δ          ⁢                                          ⁢          Q                Q            =                        -          2                ⁢                              δ            ⁢                                                  ⁢            d                    d                      ⁢                                    δ        ⁢                                  ⁢        d            d        =                  -                  1          2                    ⁢                        δ          ⁢                                          ⁢          Q                Q                        σ      ⁡              (                              δ            ⁢                                                  ⁢            d                    d                )              =                  -                  1          2                    ⁢              σ        ⁡                  (                                    δ              ⁢                                                          ⁢              Q                        Q                    )                    
The Poisson distribution of the TOF sensing procedure is:
            σ      ⁡              (                              δ            ⁢                                                  ⁢            Q                                                                      ⁢            Q                          )              ->                  1                  N                    ⁢                          ⁢      where      ⁢                          ⁢      N        =      Q    q  
The unreliability of the depth is:
      σ    ⁡          (                        δ          ⁢                                          ⁢          d                d            )        =                    -                  1          2                    ⁢                        1          N                      =          -              1                  2          ⁢          SNR                    
The formula represents the linear relationship between the unreliability of the depth and the amount of the photons. Therefore, the unreliability of the depth of the PS procedure is smaller than the unreliability of the depth of the TOF sensing procedure.
Since the signal-to-noise ration (SNR) is inversely proportional to the unreliability, the SNR of the TOF sensing procedure is less than the SNR of the PS procedure. It means that the tolerance scope of the depth measured by the TOF sensing procedure is larger than the tolerance scope of the depth measured by the PS procedure. For example, if the tolerance scope of the depth measured by the TOF sensing procedure is 0.02, the tolerance scope of the depth measured by the PS procedure may be 0.005. Therefore, the resolution of the PS procedure is higher than the resolution of the TOF sensing procedure.